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Performance Evaluation of Emerging Networks of Quantum Repeaters: Analysis and Simulation

Kobi Ravid, Javad Ghaderi, Gil Zussman

arXiv:2610.02778v1cs.NI

TL;DR

Practical quantum networks largely use DIRs and line-like fiber topologies, motivating performance evaluation that accounts for both quantum and classical components. The paper develops a hybrid simulation platform and analytical DIR analysis, finding that modest memory can limit DIR performance degradation while network memory needs depend on size and fiber lengths.

  • Problem

    Practical quantum-network deployments largely use DIRs and line-like telecommunications-fiber topologies, creating a need to evaluate EPR and average Fidelity in those settings.

    Source: §1 · p. 2

  • Method

    The paper combines a quantum-and-classical network simulator with analytical DIR performance models and evaluates line-network simulations under varied sizes, fiber lengths, and quantum errors.

    Source: §8 · p. 21

  • Results

    EPR 0.79 is maintained with memory sizes 45 and 80 for equal-length networks with one and three nodes, respectively; more nodes or uneven fiber lengths require more memory to maintain EPR.

    Source: §1 · p. 4

  • Takeaways & Limitations

    For DIR inputs with arrival probabilities 0.2 and 0.8, memory size M = 3 yields only 3% performance degradation even though expected memory utilization cannot be bounded.

    Source: §1 · p. 3

    The network model assumes a loop-free line topology, BP generation at every time unit, swapping-capable repeaters, and replacement of stored qubits when memory fills.

    Source: §3.2.1 · p. 6

Abstract

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Emerging experimental quantum network deployments are based on collaborations between research institutions and rely on telecommunications fiber infrastructure. Currently, such networks consist of mostly Dual Input Repeaters (DIRs) and can be viewed as composed of (mostly) line graphs. In order to evaluate the performance of such networks (e.g., in terms of Entangled Pair Rate, EPR, and average Fidelity) we developed a custom quantum network simulation platform that takes into account both the quantum and classical network components. To support the verification of the simulation results, we develop a novel approach for performance analysis of DIRs. We compare the simulation results to the analytical results for DIRs and to prior results for repeaters with more than two inputs. We observe that although the expected memory utilization cannot be bounded, \emph{a small DIR memory size is sufficient and leads to minimal performance degradation}. For line networks with a single repeater and $3$ repeaters, we explore the dependency of incoming and outgoing memory size requirements on the number of nodes (network size), their connectivity (fiber length) and various quantum error settings (amplitude damping and phase flip channels). We evaluate the \emph{EPR} and the \emph{average Fidelity} for a sub-network of a deployed network with $3$ repeaters, using two alternative paths. We show that as the number of nodes increases or when the fiber lengths between nodes differ significantly, additional node memory is needed to maintain the same EPR (qubits are stored for longer duration to allow completion of entanglement across the network). We also show that the memory size should be above some minimum threshold to allow EP creation (EPR $>0$) as pair selection and swapping completion propagate across the network.

1. Introduction

The paper examines practical quantum networks built largely from Dual Input Repeaters (DIRs) and line-like fiber topologies, developing a hybrid simulator and analytical methods to assess their performance. It reports that small DIR memories can limit performance degradation, while network size, fiber lengths, latency, and quantum errors affect memory needs, EPR, and Fidelity.

1. Introduction

  • Practical deployments rely on telecommunications fiber, mostly use DIRs, and can largely be represented as line graphs.More complex topologies may emerge as networks mature.Source: §1 · p. 2
  • The custom simulation platform models quantum and classical network components together, including fiber impairments, quantum losses, and classical connectivity constraints.Quantum communications and classical packets are processed jointly to support possible shared-fiber connectivity.Source: §1 · p. 3
  • For repeaters with more than two inputs, simulation results fall within 3% of the analytical results for expected memory utilization.For DIRs, the paper instead introduces a performance analysis because expected memory utilization cannot be bounded.Source: §1 · p. 3
  • M = 3 causes only 3% performance degradation for DIR inputs with arrival probabilities 0.2 and 0.8, despite unbounded expected memory utilization.The DIR analysis models performance degradation for on-the-fly and full-memory-usage pairing; its analytical predictions match simulation within 0.3%.Source: §1 · p. 3
  • Low-M single-repeater networks have low EPR due to classical-result latency, while high-M performance is sensitive to outgoing memory size.In the BNL–SBU–WBY sub-network, EPR is below 0.015 at M = 6; longer fibers increase storage time, and Fidelity degrades with high memory amplitude damping.Source: §1 · p. 4
  • In equal-length practical networks, memory sizes of 45 and 80 maintain EPR 0.79 for networks with one and three nodes, respectively.Increasing node count or having significantly different fiber lengths requires additional memory to maintain the same EPR; memory must also exceed a minimum threshold for EP creation.Source: §1 · p. 4

2. Related work

Prior work addresses quantum-network protocols, network flow and EPR optimization, memory analysis, and simulation. The paper places its custom simulator alongside this work and focuses on practical networks whose topology and memory constraints shape performance.

2. Related work

  • Proposed approaches to maximizing EPR include two-step, segmented, swapping-tree, base-graph, and QKD-oriented methods.Network-flow approaches also differ in whether they prepare the next link during qubit propagation or establish a full propagation path.Source: §2 · p. 4
  • Generic line or lattice topologies enable diverse paths, making path selection and qubit-pair prioritization part of a complex optimization problem.Multi-location testbeds use memory to compensate for timing misalignment, while limited and costly memory motivates efforts to reduce swapping wait time.Source: §2 · pp. 4–5
  • Prior CTMC and DTMC analyses address expected incoming-memory utilization; for K ≥ 3 it has a closed form, whereas for K = 2 utilization goes to infinity.The cited analyses include bipartite, tripartite, and multipartite matching.Source: §2 · p. 5
  • Unlike quantum-focused simulators such as NetSquid, the paper's custom platform incorporates classical networking alongside quantum networking.It models fiber impairments, quantum losses, and classical connectivity constraints, jointly processing quantum and classical packets.Source: §2 · p. 5

3.1. Swapping

Entanglement swapping converts Bell pairs shared with a repeater into an entangled pair shared by the remote endpoints.

3.1. Swapping

  • Alice and Bob each prepare a Bell pair and send one qubit to the repeater.The repeater applies CNOT and Hadamard gates to the received qubits before measuring them.Source: §3.1 · p. 5
  • After measurement, the repeater sends Bob a two-bit classical result over fiber.The classical message travels from the repeater to Bob.Source: §3.1 · p. 5
  • Bob applies X, Z, or both gates according to the result, yielding a shared entangled pair between Alice and Bob.Source: §3.1 · p. 5

3.2. Network model

The network model treats the end-to-end task as entanglement creation across a loop-free line, with repeater swapping shaped by memory, fiber delay, and quantum-channel effects.

3.2.1. General architecture

  • Networks designate two of N nodes as end nodes and treat the remaining nodes as repeaters; in the line case, repeaters are DIRs and end nodes have one edge.The model assumes a loop-free line, BP generation at every time unit, swapping-capable repeaters, replacement of stored qubits when memory fills, and clearing associated qubits after loss.Source: §3.2.1 · pp. 5–6

3.2.2. Network flow

  • Each iteration generates and stores Bell-pair qubits, sends them over delayed fibers, stores arrivals, selects eligible pairs, and performs swapping when possible.Classical swapping results are then sent over fiber; the simulation also exchanges management information about losses and qubits involved in swapping.Source: §3.2.2 · p. 6

3.2.3. Classical channels

  • Classical propagation delay between nodes is proportional to fiber length, using refractive index 1.444 for 1550 nm channels and the speed of light.Source: §3.2.3 · p. 6

3.2.4. Quantum channels

  • For neighboring nodes i and j, the assumed qubit-arrival probability is 0.99 × 10^(-0.2d_ij/10), reflecting 0.99 conversion success and 0.2 dB/km loss.For a 25 km fiber under close to optimal conditions (122 μs delay), the mean phase change is σϕ = 0.1 rad.Source: §3.2.4 · p. 7

3.2.5. Quantum memory

  • The model assumes EIT memories with T1 population relaxation and T2 coherence dephasing, representing amplitude damping and memory phase-flip errors.For storage time t, amplitude damping is γ = 1 − e^(−t/T1), while memory phase-flip probability is PM = (1 − λM)/2 with λM = e^(−t/T2).Source: §3.2.5 · p. 7

3.3. Single repeater model

The single-repeater model specifies probabilistic qubit arrivals from neighboring nodes and distinguishes memory-limited pairing rate from its maximum. A high-level platform view accompanies this model.

3.3. Single repeater model

  • Each neighbor sends one qubit per time unit, and the repeater receives it with node-specific probability p_k.For homogeneous links, the shared arrival probability is P, with loss probability 1 − P.Source: §3.3 · p. 7
  • For a single repeater, EPR is the pairing rate; R(M) is the rate at memory size M, bounded by Rmax.Q denotes the number of stored qubits, E[Q] the expected utilization, and Q the simulated average utilization.Source: §3.3 · p. 7
  • Figure 6 gives a high-level view of the simulation platform.Source: Figure 6 · p. 8

4. Simulation platform

The platform jointly models quantum and classical network dynamics, with configurable network components and synchronization supporting time-dependent impairments.

4. Simulation platform

  • The platform jointly handles classical and quantum packets, including fiber impairments, quantum losses, and classical connectivity constraints.This joint simulation is intended to support future hybrid connectivity over shared fibers.Source: §4 · p. 8
  • Nodes can be connected in arbitrary topologies, while a distributed master clock advances the simulation in user-defined time steps.Two nodes are designated as end nodes, and a control node manages network optimization.Source: §4 · p. 8
  • Quantum nodes coordinate memory, BP generation, interfaces, algorithms, and synchronization; quantum channels model fiber delay, loss, and impairments.Figure 7 depicts logical structures for selected components, including the quantum node, quantum channel, and control node.Source: §4 · p. 8, Figure 7 · p. 9
  • Figure 8 presents instantaneous memory utilization for a single repeater with K=3 and K=2 nodes at P=0.8.Source: Figure 8 · p. 9

5. Repeater with more than two inputs

For repeaters with at least three inputs, the paper compares simulated average memory utilization with a DTMC-based analytical estimate and reports close agreement.

5. Repeater with more than two inputs

  • For K=3 and P=0.8, simulated average memory utilization is Q=0.5350 across the three neighboring nodes.The per-node averages are 0.179, 0.1815, and 0.1745; maximum total utilization is 5, though node peaks do not coincide.Source: §5 · p. 9
  • The analysis uses a DTMC expression for expected memory utilization E[Q] when K≥3.The expression is defined through β0, the root of a function involving the input and loss probabilities.Source: §5 · p. 9
  • For varying numbers of nodes K as a function of P, simulation results Q are within 3% of analytical E[Q]; each point averages five independent runs of 1,800 iterations.Source: §5 · p. 9

6. Dual Input Repeater (DIR)

For DIRs, the paper shifts from unbounded expected memory utilization to performance degradation at finite memory, analyzing two pairing policies with DTMCs. The full-memory model agrees with simulation within 0.3%, while the on-the-fly model approximates it at high memory sizes.

6. Dual Input Repeater (DIR)

  • For K=2, expected memory utilization grows without bound, so the analysis focuses on pairing-rate degradation at a given finite memory size.The problem asks for the minimum M achieving R(M)=(1−δ)Rmax.Source: §6 · pp. 9–10
  • For K=2, the maximum pairing rate is Rmax=min(p1,p2), assuming two matched qubits and matching efficiency q=1.This rate ceiling accommodates different input probabilities.Source: §6 · p. 10

6.1. On-the-fly pairing model

  • In on-the-fly pairing, qubits are stored only when no pair can be made; a pair forms when both inputs arrive together or a stored qubit is retrieved.Source: §6 · p. 10, §6.1 · pp. 10–11
  • DTMC analysis provides pairing-rate expressions for both the on-the-fly and full-memory-usage models.The paper describes on-the-fly pairing as simpler to analyze and a close approximation to the full-memory model.Source: §6 · p. 10, §6.1 · p. 11, §6.2 · p. 13
  • For 0<ρ<1, required memory M(δ) is obtained numerically and rounded up to an integer.Source: §6.1 · p. 12, §6.2 · p. 15
  • The full-memory model stores every arriving qubit before matching, accommodating arrivals at different times or rates.Its state tracks the numbers of stored qubits originating from each input node.Source: §6.1 · p. 11, §6.2 · p. 13
  • Simulation and the full-memory-usage model agree within 0.3% across tested memory sizes and input probabilities; on-the-fly estimates are higher at high memory sizes.Figure 12 compares mean simulated pairing rate with both analytical models.Source: Figure 12 · p. 15, §6.2 · p. 15
  • With p1=0.2 and p2=0.8, M=3 gives 3% performance degradation, versus M=4 when p1=0.4 and p2=0.8.When equal input probabilities are low, more memory is required; a few percentage points of degradation can reduce memory needs.Source: §6.2 · pp. 15–16

7. Quantum network performance

The section evaluates EPR and average fidelity in synthetic and practical line networks, using a greedy swapping policy and varying network distances, repeater counts, and quantum-error settings.

7.1. Repeater swapping policy

  • The line-network policy greedily pairs valid qubits to increase post-swap distance, prioritizing Alice–Bob pairs and otherwise selecting pairs that maximize distance, with elapsed time breaking some ties.Swapping is skipped unless the post-swap distance exceeds the pre-swap distance.Source: §7.1 · pp. 16–17

7.2. SCY-QNet network graph

  • The evaluated SCY-QNet routes connect CBU and BNL through either SBU, WBY, and BKN or CMK, GCY, and BKN; the depicted subgraph gives link distances in meters.BKN is described as a DIR with 35,000 m and 62,000 m fiber links to its neighbors.Source: Figure 14 · p. 17, §7.2 · p. 17

7.3.1. λPF settings

  • Quantum-error sweeps use λPF(25) values 0.95, 0.8, and 0.6, and six [Γ1, Γ2] settings ranging from [10,000, 100,000] Hz to Hz.The phase-flip values for other fiber lengths are scaled from λPF(25) under an assumed constant relative phase noise along the fiber.Source: §7.3.1 · p. 17, §7.3.2 · p. 18

7.4. Performance of line topology network with a single repeater

  • With 1:2 fiber lengths, single-repeater memory M = 650 is needed to approach Rmax, as qubits from the shorter link wait for arrivals from the longer link.Average fidelity also decreases with increasing M, more strongly than in the common-length case.Source: §7.4 · p. 18
  • At M = 45, single-repeater EPR is 0.7 to 0.8; average fidelity exceeds 0.9 for most error cases but is sub 0.7 and 0.4 for the two stated high-memory-error cases.The two fidelity values correspond respectively to [Γ1, Γ2] = [10,000, 100,000] Hz and [333, 3,333] Hz.Source: §7.4 · p. 18, Figure 15 · p. 19
  • In three SCY-QNet sub-networks, EPR approaches Rmax at M = 25; for WBY↔BKN↔CBU it is below 0.05 versus Rmax = 0.057, about an 8% difference.The passage attributes the modest memory requirement to low arrival probability, which prevents frequent replacement of stored qubits; swapping and classical-result delays still increase memory needs relative to isolated DIR analysis.Source: §7.4 · p. 18, Figure 16 · p. 20

7.5. Performance of line topology network with three repeaters

  • For three repeaters with equal 4,630 m links, memory must exceed M = 35 to enable end-to-end EP creation, and larger memory moves EPR toward Rmax = 0.8.Below the minimum, qubits can be replaced before an end-to-end EP is created; high Γ1 also produces fidelity values of 0.5.Source: §7.5 · p. 19, Figure 17 · p. 20
  • For M = 30, path option 1 yields EPR 0.011 to 0.014 and path option 2 yields 0.01 to 0.015; path 1 fidelity falls from 0.6−0.7 to 0.3−0.35 as memory errors rise.The fidelity comparison fixes λPF(25) = 0.95; the EPR ranges are reported for both path options.Source: §7.5 · p. 19, Figure 18 · p. 21

8. Conclusion and Future Work

The paper validates its simulation platform and introduces an analytical DIR performance model, then evaluates line-network EPR and fidelity. Its results emphasize memory-size tradeoffs, network latency, and quantum errors, while identifying several areas for future model and policy work.

8. Conclusion and Future Work

  • The DIR analysis models performance degradation against memory size for on-the-fly and full-memory-usage pairing; simulation matches the predicted degradation, with M = 3 causing only 3% degradation for arrival probabilities 0.2 and 0.8.The authors conclude that small memory can approach maximum EPR despite unbounded expected memory utilization.Source: §8 · p. 21
  • Across line networks, memory requirements depend on network latency and losses, while fidelity degrades with longer fibers and higher memory-error rates; population loss can produce fidelity 0.5.The conclusion also reports that unequal fiber lengths can require higher M to approach Rmax, while single-repeater average fidelity exceeds 0.9 for most quantum-error cases.Source: §8 · pp. 21–22
  • Future work includes optimizing incoming and outgoing memory queues, testing alternative storage policies and timing-offset handling, and extending evaluations beyond line topologies.The authors note that only limited alternative paths exist between specific endpoints and describe their two-path approach as simplified and potentially suboptimal.Source: §8 · p. 22
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